Simplify line about pygeoif HOT 3 CLOSED

def rdp(points, epsilon):
    """Ramer-Douglas-Peucker algorithm to simplify a line.

    Args:
        points (list): A list of (x, y) tuples representing a line.
        epsilon (float): Maximum distance between a point and the simplified line.

    Returns:
        A simplified list of (x, y) tuples.
    """
    if len(points) <= 2:
        return points

    # Find the point with the maximum distance from the line
    dmax = 0
    index = 0
    for i in range(1, len(points)-1):
        d = point_to_line_distance(points[i], points[0], points[-1])
        if d > dmax:
            index = i
            dmax = d

    # If the maximum distance is greater than epsilon, recursively simplify the line
    if dmax > epsilon:
        # Simplify the line before the index
        simplified1 = rdp(points[:index+1], epsilon)
        # Simplify the line after the index
        simplified2 = rdp(points[index:], epsilon)
        # Combine the simplified lines
        simplified = simplified1[:-1] + simplified2
    else:
        simplified = [points[0], points[-1]]

    return simplified

def point_to_line_distance(point, start, end):
    """Calculate the distance between a point and a line.

    Args:
        point (tuple): A (x, y) tuple representing the point.
        start (tuple): A (x, y) tuple representing the start of the line.
        end (tuple): A (x, y) tuple representing the end of the line.

    Returns:
        The distance between the point and the line.
    """
    x, y = point
    x1, y1 = start
    x2, y2 = end
    numerator = abs((y2-y1)*x - (x2-x1)*y + x2*y1 - y2*x1)
    denominator = ((y2-y1)**2 + (x2-x1)**2)**0.5
    return numerator / denominator

>>> points = [(0, 0), (1, 1), (2, 2), (3, 1), (4, 0)]
>>> simplified = rdp(points, 0.5)
>>> print(simplified)
[(0, 0), (2, 2), (4, 0)]

def simplify_vw(points, threshold):
    # Compute the effective area (triangle formed by the adjacent points)
    areas = []
    for i in range(1, len(points) - 1):
        a, b, c = points[i-1:i+2]
        areas.append(abs((b[0] - a[0]) * (c[1] - a[1]) - (c[0] - a[0]) * (b[1] - a[1])))

    # Compute the simplification priority (smallest area)
    priorities = dict(zip(range(1, len(points) - 1), areas))
    sorted_priorities = sorted(priorities.items(), key=lambda x: x[1])

    # Simplify the line
    while sorted_priorities:
        index, priority = sorted_priorities.pop()

        if priority > threshold:
            break

        del points[index]

        if index > 1:
            areas[index-2] = abs((points[index-2][0] - points[index-1][0]) * (points[index][1] - points[index-2][1]) - (points[index][0] - points[index-2][0]) * (points[index-1][1] - points[index-2][1]))
            priorities[index-1] = areas[index-2]
            sorted_priorities = sorted(priorities.items(), key=lambda x: x[1])

    return points